High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin code. he recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-Lagrangian schemes (which are usually based on polynomial or spline interpolation). In this paper, we consider a parallel implementation of a semi-Lagrangian discontinuous Galerkin method for distributed memory systems (so-called clusters). Both strong and weak scaling studies are performed on the Vienna Scientific Cluster 2 (VSC-2). In the case of weak scaling we observe a parallel efficiency above 0.8 for both two and four dimensional problems and up to 8192 cores. Strong scaling results show good scalability to at least 512 cores (we consider problems that can be run on a single processor in reasonable time). In addition, we study the scaling of a two dimensional Vlasov-Poisson solver that is implemented using the framework provided. All of the simulations are conducted in the context of worst case communication overhead; i.e., in a setting where the CFL (Courant-Friedrichs-Lewy) number increases linearly with the problem size. The framework introduced in this paper facilitates a dimension independent implementation of scientific codes (based on C++ templates) using both an MPI and a hybrid approach to parallelization. We describe the essential ingredients of our implementation.
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References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
- Ding, Zhiyan; Einkemmer, Lukas; Li, Qin: Dynamical low-rank integrator for the linear Boltzmann equation: error analysis in the diffusion limit (2021)
- Crouseilles, Nicolas; Einkemmer, Lukas; Massot, Josselin: Exponential methods for solving hyperbolic problems with application to collisionless kinetic equations (2020)
- Einkemmer, Lukas; Ostermann, Alexander; Piazzola, Chiara: A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction (2020)
- Einkemmer, Lukas: A performance comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensions (2019)
- Einkemmer, Lukas; Lubich, Christian: A quasi-conservative Dynamical Low-rank algorithm for the Vlasov equation (2019)
- Einkemmer, Lukas; Lubich, Christian: A low-rank projector-splitting integrator for the Vlasov-Poisson equation (2018)
- Einkemmer, Lukas; Ostermann, Alexander: A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev-Petviashvili equation (2018)
- Einkemmer, Lukas: High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin code (2016)